/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.hs /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


H-Termination with start terms of the given HASKELL could be proven:

(0) HASKELL
(1) BR [EQUIVALENT, 0 ms]
(2) HASKELL
(3) COR [EQUIVALENT, 0 ms]
(4) HASKELL
(5) Narrow [EQUIVALENT, 27 ms]
(6) YES


----------------------------------------

(0)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data Integer = Integer MyInt ;

data MyInt = Pos Main.Nat  | Neg Main.Nat ;

data Main.Nat = Succ Main.Nat  | Zero ;

data Ratio a = CnPc a a ;

fromIntMyInt :: MyInt  ->  MyInt;
fromIntMyInt x = x;

fromIntegerMyInt :: Integer  ->  MyInt;
fromIntegerMyInt (Integer x) = x;

fromIntegerRatio :: Integer  ->  Ratio MyInt;
fromIntegerRatio x = CnPc (fromIntegerMyInt x) (fromIntMyInt (Main.Pos (Main.Succ Main.Zero)));

fromIntegral = pt fromIntegerRatio toIntegerMyInt;

pt :: (a  ->  c)  ->  (b  ->  a)  ->  b  ->  c;
pt f g x = f (g x);

toIntegerMyInt :: MyInt  ->  Integer;
toIntegerMyInt x = Integer x;

}

----------------------------------------

(1) BR (EQUIVALENT)
Replaced joker patterns by fresh variables and removed binding patterns.
----------------------------------------

(2)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data Integer = Integer MyInt ;

data MyInt = Pos Main.Nat  | Neg Main.Nat ;

data Main.Nat = Succ Main.Nat  | Zero ;

data Ratio a = CnPc a a ;

fromIntMyInt :: MyInt  ->  MyInt;
fromIntMyInt x = x;

fromIntegerMyInt :: Integer  ->  MyInt;
fromIntegerMyInt (Integer x) = x;

fromIntegerRatio :: Integer  ->  Ratio MyInt;
fromIntegerRatio x = CnPc (fromIntegerMyInt x) (fromIntMyInt (Main.Pos (Main.Succ Main.Zero)));

fromIntegral = pt fromIntegerRatio toIntegerMyInt;

pt :: (c  ->  b)  ->  (a  ->  c)  ->  a  ->  b;
pt f g x = f (g x);

toIntegerMyInt :: MyInt  ->  Integer;
toIntegerMyInt x = Integer x;

}

----------------------------------------

(3) COR (EQUIVALENT)
Cond Reductions:
The following Function with conditions
"undefined |Falseundefined;
"
is transformed to
"undefined  = undefined1;
"
"undefined0 True = undefined;
"
"undefined1  = undefined0 False;
"

----------------------------------------

(4)
Obligation:
mainModule Main 
module Main where {
import qualified Prelude;
data Integer = Integer MyInt ;

data MyInt = Pos Main.Nat  | Neg Main.Nat ;

data Main.Nat = Succ Main.Nat  | Zero ;

data Ratio a = CnPc a a ;

fromIntMyInt :: MyInt  ->  MyInt;
fromIntMyInt x = x;

fromIntegerMyInt :: Integer  ->  MyInt;
fromIntegerMyInt (Integer x) = x;

fromIntegerRatio :: Integer  ->  Ratio MyInt;
fromIntegerRatio x = CnPc (fromIntegerMyInt x) (fromIntMyInt (Main.Pos (Main.Succ Main.Zero)));

fromIntegral = pt fromIntegerRatio toIntegerMyInt;

pt :: (b  ->  a)  ->  (c  ->  b)  ->  c  ->  a;
pt f g x = f (g x);

toIntegerMyInt :: MyInt  ->  Integer;
toIntegerMyInt x = Integer x;

}

----------------------------------------

(5) Narrow (EQUIVALENT)
Haskell To QDPs

digraph dp_graph {
node [outthreshold=100, inthreshold=100];1[label="fromIntegral",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
3[label="fromIntegral vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
4[label="pt fromIntegerRatio toIntegerMyInt vx3",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
5[label="fromIntegerRatio (toIntegerMyInt vx3)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
6[label="CnPc (fromIntegerMyInt (toIntegerMyInt vx3)) (fromIntMyInt (Pos (Succ Zero)))",fontsize=16,color="green",shape="box"];6 -> 7[label="",style="dashed", color="green", weight=3];
6 -> 8[label="",style="dashed", color="green", weight=3];
7[label="fromIntegerMyInt (toIntegerMyInt vx3)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
8[label="fromIntMyInt (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
9[label="fromIntegerMyInt (Integer vx3)",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
10[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];11[label="vx3",fontsize=16,color="green",shape="box"];}

----------------------------------------

(6)
YES